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Diffusion-weighted magnetic resonance imaging (dMRI) is a non-invasive technique to probe the complex micro-architecture of the tissue being imaged. The diffusional properties of the tissue at the imaged resolution are well captured by the ensemble average propagator (EAP), which is a probability density function characterizing the probability of water molecule diffusion. Many properties in the form of imaging 'stains' can then be computed from the EAP that can serve as bio-markers for a variety of diseases. This motivates the development of methods for the accurate estimation of the EAPs from dMRI, which is an actively researched area in dMRI analysis. To this end, in the recent past, dictionary learning (DL) techniques have been applied by many researchers for accurate reconstruction of the EAP fields from dMRI scans of the central nervous system (CNS). However, most of the DL-based methods did not exploit the geometry of the space of the EAPs, which are probability density functions. By exploiting the geometry of the space of probability density functions, it is possible to reconstruct EAPs that satisfy the mathematical properties of a density function and hence yield better accuracy in the EAP field reconstruction. Using a square root density parameterization, the EAPs can be mapped to a unit Hilbert sphere, which is a smooth manifold with well known geometry that we will exploit in our formulation of the DL problem. Thus, in this paper, we present a general formulation of the DL problem for data residing on smooth manifolds and in particular the manifold of EAPs, along with a numerical solution using an alternating minimization method. We then showcase the properties and the performance of our algorithm on the reconstruction of the EAP field in a patch-wise manner from the dMRI data. Through several synthetic, phantom and real data examples, we demonstrate that our non-linear DL-based approach produces accurate and spatially smooth estimates of the EAP field from dMRI in comparison to the state-of-the-art EAP reconstruction method called the MAPL method, as well as the linear DL-based EAP reconstruction approaches. To further demonstrate the accuracy and utility of our approach, we compute an entropic anisotropy measure (HA), that is a function of the well known Rényi entropy, from the EAP fields of control and injured rat spinal cords respectively. We demonstrate its utility as an imaging 'stain' via a quantitative comparison of HA maps computed from EAP fields estimated using our method and competing methods. The quantitative comparison is achieved using a two sample t-test and the results of significance are displayed for a visualization of regions of the spinal cord affected most by the injury.

Numerous methods such as adding different eccentric and concentric braces, steel or concrete shear walls, etc. are used to strengthen reinforced concrete (RC) frames. If the seismic characteristics of the hybrid seismic resistant system are not known, choosing the suitable system for strengthening would be difficult. In this paper, the behavior of a moment resisting reinforced concrete frame strengthened with partially attached steel infill plate subjected to cyclic lateral loads has been investigated. The assessment has been carried out through an experimental approach with conventional and perforated steel infill plates. Five moment resisting reinforced concrete frames with identical dimensions, steel content, and concrete strength were built with the scale of 1:3. Among the four samples, two incorporated perforated, partially attached infill plates and the other two were strengthened with conventional partially attached steel infill plates. Finally, the cracking pattern, effective stiffness, strength reduction factors, ductilities, ultimate strengths, and energy absorption capacities of all the samples were calculated and compared. The results show that using partially attached steel infill plate causes the cracking pattern of the strengthened frame to be almost similar to that of the initial frame. In addition, the perforated steel infill plate not only increases the stiffness and lateral strength of the frame, it also increases the strength reduction factor by 35%.

Climate change affects human health; however, there have been no large-scale, systematic efforts to quantify the heat-related human health impacts that have already occurred due to climate change. Here, we use empirical data from 732 locations in 43 countries to estimate the mortality burdens associated with the additional heat exposure that has resulted from recent human-induced warming, during the period 1991–2018. Across all study countries, we find that 37.0% (range 20.5–76.3%) of warm-season heat-related deaths can be attributed to anthropogenic climate change and that increased mortality is evident on every continent. Burdens varied geographically but were of the order of dozens to hundreds of deaths per year in many locations. Our findings support the urgent need for more ambitious mitigation and adaptation strategies to minimize the public health impacts of climate change., We thank the participants of the ISIMIP Health workshop in Barcelona in November 2018 where this work was discussed for the first time. This study was supported by the Medical Research Council UK (grant no. MR/M022625/1), the Natural Environment Research Council UK (grant no. NE/R009384/1) and the European Union’s Horizon 2020 Project Exhaustion (grant no. 820655). N.S. was supported by the NIEHS-funded HERCULES Center (P30ES019776). Y.H. was supported by the Environment Research and Technology Development Fund of the Environmental Restoration and Conservation Agency, Japan (JPMEERF15S11412). J.J.J.K.J. was supported by Academy of Finland (grant no. 310372). V.H. was supported by the Spanish Ministry of Economy, Industry and Competitiveness (grant no. PCIN-2017-046) and the German Federal Ministry of Education and Research (grant no. 01LS1201A2). J.K. and A.U. were supported by the Czech Science Foundation (grant no. 20-28560S). J.M. was supported by the Fundação para a Ciência e a Tecnologia (FCT) (SFRH/BPD/115112/2016). S.R. and F.d.R. were supported by European Union’s Horizon 2020 Project EXHAUSTION (grant no. 820655). M.H. was supported by the Japan Science and Technology Agency as part of SICORP, grant no. JPMJSC20E4. Y.G. was supported by the Career Development Fellowship of the Australian National Health and Medical Research Council (APP1163693). S.L. was support by the Early Career Fellowship of the Australian National Health and Medical Research Council (APP1109193). Y.L.L.G. was supported by the Taiwan Ministry of Science and Technology (MOST110-2918-I-002-007) as a visiting academic at the University of Sydney.

Many regions of the world are now facing more frequent and unprecedentedly large wildfires. However, the association between wildfire-related PMFor this time series study, data on daily counts of deaths for all causes, cardiovascular causes, and respiratory causes were collected from 749 cities in 43 countries and regions during 2000-16. Daily concentrations of wildfire-related PM65·6 million all-cause deaths, 15·1 million cardiovascular deaths, and 6·8 million respiratory deaths were included in our analyses. The pooled RRs of mortality associated with each 10 μg/mShort-term exposure to wildfire-related PMAustralian Research Council, Australian National HealthMedical Research Council.

Background: Exposure to cold or hot temperatures is associated with premature deaths. We aimed to evaluate the global, regional, and national mortality burden associated with non-optimal ambient temperatures. Methods: In this modelling study, we collected time-series data on mortality and ambient temperatures from 750 locations in 43 countries and five meta-predictors at a grid size of 0·5° × 0·5° across the globe. A three-stage analysis strategy was used. First, the temperature–mortality association was fitted for each location by use of a time-series regression. Second, a multivariate meta-regression model was built between location-specific estimates and meta-predictors. Finally, the grid-specific temperature–mortality association between 2000 and 2019 was predicted by use of the fitted meta-regression and the grid-specific meta-predictors. Excess deaths due to non-optimal temperatures, the ratio between annual excess deaths and all deaths of a year (the excess death ratio), and the death rate per 100 000 residents were then calculated for each grid across the world. Grids were divided according to regional groupings of the UN Statistics Division. Findings: Globally, 5 083 173 deaths (95% empirical CI [eCI] 4 087 967–5 965 520) were associated with non-optimal temperatures per year, accounting for 9·43% (95% eCI 7·58–11·07) of all deaths (8·52% [6·19–10·47] were cold-related and 0·91% [0·56–1·36] were heat-related). There were 74 temperature-related excess deaths per 100 000 residents (95% eCI 60–87). The mortality burden varied geographically. Of all excess deaths, 2 617 322 (51·49%) occurred in Asia. Eastern Europe had the highest heat-related excess death rate and Sub-Saharan Africa had the highest cold-related excess death rate. From 2000–03 to 2016–19, the global cold-related excess death ratio changed by −0·51 percentage points (95% eCI −0·61 to −0·42) and the global heat-related excess death ratio increased by 0·21 percentage points (0·13–0·31), leading to a net reduction in the overall ratio. The largest decline in overall excess death ratio occurred in South-eastern Asia, whereas excess death ratio fluctuated in Southern Asia and Europe. Interpretation: Non-optimal temperatures are associated with a substantial mortality burden, which varies spatiotemporally. Our findings will benefit international, national, and local communities in developing preparedness and prevention strategies to reduce weather-related impacts immediately and under climate change scenarios. Funding: Australian Research Council and the Australian National Health and Medical Research Council.

Summary Background Many regions of the world are now facing more frequent and unprecedentedly large wildfires. However, the association between wildfire-related PM2·5 and mortality has not been well characterised. We aimed to comprehensively assess the association between short-term exposure to wildfire-related PM2·5 and mortality across various regions of the world. Methods For this time series study, data on daily counts of deaths for all causes, cardiovascular causes, and respiratory causes were collected from 749 cities in 43 countries and regions during 2000–16. Daily concentrations of wildfire-related PM2·5 were estimated using the three-dimensional chemical transport model GEOS-Chem at a 0·25° × 0·25° resolution. The association between wildfire-related PM2·5 exposure and mortality was examined using a quasi-Poisson time series model in each city considering both the current-day and lag effects, and the effect estimates were then pooled using a random-effects meta-analysis. Based on these pooled effect estimates, the population attributable fraction and relative risk (RR) of annual mortality due to acute wildfire-related PM2·5 exposure was calculated. Findings 65·6 million all-cause deaths, 15·1 million cardiovascular deaths, and 6·8 million respiratory deaths were included in our analyses. The pooled RRs of mortality associated with each 10 μg/m3 increase in the 3-day moving average (lag 0–2 days) of wildfire-related PM2·5 exposure were 1·019 (95% CI 1·016–1·022) for all-cause mortality, 1·017 (1·012–1·021) for cardiovascular mortality, and 1·019 (1·013–1·025) for respiratory mortality. Overall, 0·62% (95% CI 0·48–0·75) of all-cause deaths, 0·55% (0·43–0·67) of cardiovascular deaths, and 0·64% (0·50–0·78) of respiratory deaths were annually attributable to the acute impacts of wildfire-related PM2·5 exposure during the study period., Australian Research Council, Australian National Health & Medical Research Council.

Possible future climatic changes can be regarded as one of the greatest challenges for planning in the current area. With a documentary-statistical approach, the present research was carried out in the central and southern regions of Iran. Initially, in the long term, the condition of the climate variability was taken into account and then future climate changes in date palm cultivation areas were projected. Based on the observational data, the years between 1985 and 2015 were recognized as the baseline period. For the future period, the output of the CMIP5 simulating model under RCP scenarios in the MarkSimGCM database was utilized. Based on the trend analysis done through the Mann-Kendal test, the results revealed a significant increasing trend in the climate parameters having an impact on Iran date palm cultivation areas in the baseline period. This increasing trend is of high significance for the temperature components such as maximum and minimum temperatures, hot days, and the heat accumulation. In the light of the projected data in the adjacent areas and higher latitudes in the central Iran, the evaluation of the effective climatic parameters uncovered that heat potentials in terms of maximum and minimum temperatures and heat potential from growing degree-days exist for the cultivation of date palm trees. In fact, based on the climatic monitoring conducted through simulated data in the regions adjacent to date palm cultivation, 3,913,444,190 ha will be extended to the date palm cultivation areas in the central region of Iran in the future (i.e., till 2081).

Exposure to suboptimal ambient temperature during pregnancy has been reported as a potential teratogen of fetal development. However, limited animal evidence is available regarding the impact of extreme temperatures on maternal pregnancy and the subsequent adverse pregnancy outcomes. Our objective in this study is to investigate the relationship between temperature and maternal stress during pregnancy in mice. This study used the Naval Medical Research Institute (NMRI) mice during the second and third pregnant weeks with the gestational day (GD) (GD 6.5–14.5 and GD 14.5–17.5). Mice were exposed to suboptimal ambient temperature (1 °C, 5 °C, 10 °C, 15 °C, 40 °C, 42 °C, 44 °C, 46 °C, and 48 °C for the experimental group and 23 °C for the control group) 1 h per day, 7 days a weekin each trimester. Measurements of placental development (placental weight [PW] and placental diameter [PD]) and fetal growth (fetal weight [FW] and crown-to-rump length [CRL]) between experimental and control groups were compared using analysis of variance (ANOVA). Data on the occurrence of preterm birth (PTB) and abnormalities were also collected. The results showed that exposure to both cold and heat stress in the second and third weeks of pregnancy caused significant decreases in measurements of placental development (PW and PD) and fetal growth (FW and CRL). For all temperature exposures, 15 °C was identified as the optimal temperature in the development of the embryo. Most PTB occurrences were observed in high-temperature stress groups, with the highest PTB number seen in the exposure group at 48 °C, whereas PTB occurred only at 1 °C among cold stress groups. In the selected exposure experiments, an approximate U-shaped relation was observed between temperature and number of abnormality occurrence. The highest percentage of these anomalies occurred at temperatures of 1 °C and 48 °C, while no abnormalities were observed at 15 °C and in the control group. Our findings strengthened the evidence that exposure to suboptimal ambient temperatures may trigger adverse pregnancy outcomes and worsen embryo and fetal development in mice.

The key aspect of parallel-beam X-ray CT is forward and back projection, but its computational burden continues to be an obstacle for applications. We propose a method to improve the performance of related algorithms by calculating the Gram filter exactly and interpolating the sinogram signal optimally. In addition, the detector blur effect can be included in our model efficiently. The improvements in speed and quality for back projection and iterative reconstruction are shown in our experiments on both analytical phantoms and real CT images.

We present a nonparametric statistical framework for the quantification, analysis, and propagation of data uncertainty in direct volume rendering (DVR). The state-of-the-art statistical DVR framework allows for preserving the transfer function (TF) of the ground truth function when visualizing uncertain data; however, the existing framework is restricted to parametric models of uncertainty. In this paper, we address the limitations of the existing DVR framework by extending the DVR framework for nonparametric distributions. We exploit the quantile interpolation technique to derive probability distributions representing uncertainty in viewing-ray sample intensities in closed form, which allows for accurate and efficient computation. We evaluate our proposed nonparametric statistical models through qualitative and quantitative comparisons with the mean-field and parametric statistical models, such as uniform and Gaussian, as well as Gaussian mixtures. In addition, we present an extension of the state-of-the-art rendering parametric framework to 2D TFs for improved DVR classifications. We show the applicability of our uncertainty quantification framework to ensemble, downsampled, and bivariate versions of scalar field datasets., Comment: 11 pages,13 figures, accepted at the IEEE VIS 2020 conference

Due to the lack of sufficient concrete strength or change in design codes, some RC structures are in need of retrofitting. Retrofitting and reevaluating a building is only possible if the seismic characteristics of the new hybrid seismic system are specified. This study attempts to experimentally investigate the effect of using the Chevron brace with ADAS and TADAS yielding dampers in retrofitting RC moment resisting frames. Seven RC moment resisting frames were constructed and six of which were retrofitted with Chevron braces and a different number of ADAS or TADAS yielding dampers. The frames were subjected to cyclic loading and strength, crack expansion, stiffness, ductility, energy dissipation, and strength reduction factor of all the frames were evaluated. The results show that the yielding dampers not only increase the strength of the RC frame, they also elevate its strength reduction factor and ductility. The effect of the ADAS damper is better than the TADAS damper and in both cases, pinching in the hysteresis diagram has considerably decreased.

Due to lack of sufficient concrete strength or change in design guidelines, some RC structures are in need of retrofitting. In the past few decades, using steel braces as a means with which to retrofit RC structures has become the subject of more attention and the reason can be attributed to fast implementation of the system as well as a significant increase in the stiffness and the strength of the structure. By adding different types of braces to moment resisting RC frames, the seismic properties of the structure including its ductility, strength reduction factor, stiffness, and strength undergo change. Retrofitting a building and designing it is only possible if the behavioral properties of the new hybrid seismic resisting system are known. This study experimentally investigates the effect of adding different types of steel braces on the behavioral properties of RC moment resisting frames. Eight RC moment resisting frames with identical steel bar configuration and concrete strength were built and seven of which were retrofitted with different braces such as the X, the knee, the chevron, the eccentric brace and the chevron brace with a vertical link. All the frames were subject to cyclic loading and their hysteresis load-displacement diagrams were plotted. Strength, stiffness, crack expansion, ductility, energy dissipation, and the strength reduction factor of all the frames were assessed. From the ductility and strength reduction factor viewpoints, the results indicate that the eccentric brace has a better performance compared to the other specimens. However, from the stiffness, strength, and cracking control standpoints, the behavior of the X brace is more desirable.

Sparse signal recovery from limited and/or degraded samples is fundamental to many applications, such as medical imaging, remote sensing, astronomical and seismic imaging. Discrete wavelet transform (DWT) has been commonly used for sparse representation of signals; nevertheless, due to its shift-variant nature, pseudo-Gibbs artifacts are present in the recovered signals. Using the redundant shift-invariant wavelet transform (SWT) is the ideal solution to obtain shift invariance; however, high redundancy factor of SWT limits its application in practical settings. We propose a dictionary splitting approach for sparse recovery from incomplete data, which leverages the ideas of cycle spinning in combination with Bregman splitting. The proposed method significantly improves the conventional signal reconstruction with DWT, offers the advantages of SWT, and overcomes high redundancy factor of SWT. We solve parallel sparse recovery problems with orthogonal dictionaries (DWT and its permuted versions), while we impose consistency between the results by updating the recovered image at each iteration. Our experiments demonstrate that few shifts are sufficient to achieve reconstruction accuracy as high as recovery with SWT, and significantly reduces its computational cost and redundancy factor.

We provide an interactive tool for extracting exemplar isosurfaces from a 3D scalareld using a novel isovalue classication process.We propose a structural VQA metric that uses representative isosurfaces as benchmark structures to assess the visual quality of compressed 3D scalarelds.Our experiments on a number of benchmark data sets suggest that, compared to existing methods, the proposed isovalue classication approach provides a more distinct set of isosurfaces that are more representative of the complexity of the datasets.We examine a number of widely-used compression techniques (i.e.,discrete wavelet transform, discrete cosine transform, and tensor approximation) to establish the utility of our VQA approach. Display Omitted Visualization of volumetric data has been widely used for exploration of data from scientific simulations and biomedical imaging. Despite advances of GPU-assisted rendering, which has become the state-of-art in direct volume rendering, still many volumetric data sets are too large to be visualized interactively. Therefore, compression-domain rendering approaches are used in visualization processes in order to reduce the amount of data sent to the GPU and thus speed up interactive visualization. Hence, reliable tools to assess the quality of the reconstructed 3D data are of great importance, influencing the effectiveness of the visualization. However, numerical error analysis approaches such as mean-squared-based metrics are often inconsistent with perceived visual quality. We propose a structural volume quality assessment approach for 3D scalar volume based on the human visual system (HVS). Our approach consists of two stages: First, we provide an interactive tool for extracting significant volume features via isosurfaces from a 3D scalar field using an isovalue classification process. Second, we propose a structural volume quality assessment (VQA) metric that employs representative isosurfaces as benchmark structures. For this purpose, we use a recently developed perceptual-based mesh quality metric [1] to assess the visual quality of compressed 3D scalar fields. Our experiments on a number of benchmark data sets suggest that, compared to existing methods, the proposed isovalue classification approach provides a more distinct set of isosurfaces that are more representative of the complexity of the data sets. We examine a number of widely used compression approaches, namely, discrete wavelet transform, discrete cosine transform, and tensor approximation, to establish the utility of our volume quality assessment approach.

The article's abstract is no available.

The pixel- and voxel-basis are common choices for image discretization in the context of computed tomography (CT). They can also be viewed as first-order box splines – a class of functions with closed-form X-ray and Radon transforms that can be computed efficiently. In this paper we derive a method for exact projection of box splines in a non-parallel geometry that can be used in fan-beam and cone-beam tomographic image reconstruction algorithms. We also provide efficient computational procedures for evaluation of the basis function in the projection domain.

The problem of isosurface extraction in uncertain data is an important research problem and may be approached in two ways. One can extract statistics (e.g., mean) from uncertain data points and visualize the extracted field. Alternatively, data uncertainty, characterized by probability distributions, can be propagated through the isosurface extraction process. We analyze the impact of data uncertainty on topology and geometry extraction algorithms. A novel, edge-crossing probability based approach is proposed to predict underlying isosurface topology for uncertain data. We derive a probabilistic version of the midpoint decider that resolves ambiguities that arise in identifying topological configurations. Moreover, the probability density function characterizing positional uncertainty in isosurfaces is derived analytically for a broad class of nonparametric distributions. This analytic characterization can be used for efficient closed-form computation of the expected value and variation in geometry. Our experiments show the computational advantages of our analytic approach over Monte-Carlo sampling for characterizing positional uncertainty. We also show the advantage of modeling underlying error densities in a nonparametric statistical framework as opposed to a parametric statistical framework through our experiments on ensemble datasets and uncertain scalar fields.

Numerical Weather Prediction (NWP) ensembles are commonly used to assess the uncertainty and confidence in weather forecasts. Spaghetti plots are conventional tools for meteorologists to directly examine the uncertainty exhibited by ensembles, where they simultaneously visualize isocontours of all ensemble members. To avoid visual clutter in practical usages, one needs to select a small number of informative isovalues for visual analysis. Moreover, due to the complex topology and variation of ensemble isocontours, it is often a challenging task to interpret the spaghetti plot for even a single isovalue in large ensembles. In this paper, we propose an interactive framework for uncertainty visualization of weather forecast ensembles that significantly improves and expands the utility of spaghetti plots in ensemble analysis. Complementary to state-of-the-art methods, our approach provides a complete framework for visual exploration of ensemble isocontours, including isovalue selection, interactive isocontour variability exploration, and interactive sub-region selection and re-analysis. Our framework is built upon the high-density clustering paradigm, where the mode structure of the density function is represented as a hierarchy of nested subsets of the data. We generalize the high-density clustering for isocontours and propose a bandwidth selection method for estimating the density function of ensemble isocontours. We present novel visualizations based on high-density clustering results, called the mode plot and the simplified spaghetti plot. The proposed mode plot visually encodes the structure provided by the high-density clustering result and summarizes the distribution of ensemble isocontours. It also enables the selection of subsets of interesting isocontours, which are interactively highlighted in a linked spaghetti plot for providing spatial context. To provide an interpretable overview of the positional variability of isocontours, our system allows for selection of informative isovalues from the simplified spaghetti plot. Due to the spatial variability of ensemble isocontours, the system allows for interactive selection and focus on sub-regions for local uncertainty and clustering re-analysis. We examine a number of ensemble datasets to establish the utility of our approach and discuss its advantages over state-of-the-art visual analysis tools for ensemble data.

Transfer function (TF) design is a central topic in direct volume rendering. The TF fundamentally translates data values into optical properties to reveal relevant features present in the volumetric data. We propose a semi-automatic TF design scheme which consists of two steps: First, we present a clustering process within 1D/2D TF domain based on the proximities of the respective volumetric features in the spatial domain. The presented approach provides an interactive tool that aids users in exploring clusters and identifying features of interest (FOI). Second, our method automatically generates a TF by iteratively refining the optical properties for the selected features using a novel feature visibility measurement. The proposed visibility measurement leverages the similarities of features to enhance their visibilities in DVR images. Compared to the conventional visibility measurement, the proposed feature visibility is able to efficiently sense opacity changes and precisely evaluate the impact of selected features on resulting visualizations. Our experiments validate the effectiveness of the proposed approach by demonstrating the advantages of integrating feature similarity into the visibility computations. We examine a number of datasets to establish the utility of our approach for semi-automatic TF design.

Accurate reconstruction of the ensemble average propagators (EAPs) from undersampled diffusion MRI (dMRI) measurements is a well-motivated, actively researched problem in the field of dMRI acquisition and analysis. A number of approaches based on compressed sensing (CS) principles have been developed for this problem, achieving a considerable acceleration in the acquisition by leveraging sparse representations of the signal. Most recent methods in literature apply undersampling techniques in the (k, q)-space for the recovery of EAP in the joint (x, r)-space. Yet, the majority of these methods follow a pipeline of first reconstructing the diffusion images in the (x, q)-space and subsequently estimating the EAPs through a 3D Fourier transform. In this work, we present a novel approach to achieve the direct reconstruction of P(x, r) from partial (k, q)-space measurements, with geometric constraints involving the parallelism of level-sets of diffusion images from proximal q-space points. By directly reconstructing P(x, r)) from (k, q)-space data, we exploit the incoherence between the 6D sensing and reconstruction domains to the fullest, which is consistent with the CS-theory. Further, our approach aims to utilize the inherent structural similarity (parallelism) of the level-sets in the diffusion images corresponding to proximally-located q-space points in a CS framework to achieve further reduction in sample complexity that could facilitate faster acquisition in dMRI. We compare the proposed method to a state-of-the-art CS based EAP reconstruction method (from joint (k, q)-space) on simulated, phantom and real dMRI data demonstrating the benefits of exploiting the structural similarity in the q-space.

This paper presents a method to build a saliency map in a volumetric dataset using 3D eye tracking. Our approach acquires the saliency information from multiple views of a 3D dataset with an eye tracker and constructs the 3D saliency volume from the gathered 2D saliency information using a tomographic reconstruction algorithm. Our experiments, on a number of datasets, show the effectiveness of our approach in identifying salient 3D features that attract user’s attention. The obtained 3D saliency volume provides importance information and can be used in various applications such as illustrative visualization.

In this paper, we investigate compressed sensing principles to devise an in-situ data reduction framework for visualization of volumetric datasets. We exploit the universality of the compressed sensing framework and show that the proposed method offers a refinable data reduction approach for volumetric datasets. The accurate reconstruction is obtained from partial Fourier measurements of the original data that are sensed without any prior knowledge of specific feature domains for the data. Our experiments demonstrate the superiority of surfacelets for efficient representation of volumetric data. Moreover, we establish that the accuracy of reconstruction can further improve once a more effective basis for a sparser representation of the data becomes available.

With uncertainty present in almost all modalities of data acquisition, reduction, transformation, and representation, there is a growing demand for mathematical analysis of uncertainty propagation in data processing pipelines. In this paper, we present a statistical framework for quantification of uncertainty and its propagation in the main stages of the visualization pipeline. We propose a novel generalization of Irwin-Hall distributions from the statistical viewpoint of splines and box-splines, that enables interpolation of random variables. Moreover, we introduce a probabilistic transfer function classification model that allows for incorporating probability density functions into the volume rendering integral. Our statistical framework allows for incorporating distributions from various sources of uncertainty which makes it suitable in a wide range of visualization applications. We demonstrate effectiveness of our approach in visualization of ensemble data, visualizing large datasets at reduced scale, iso-surface extraction, and visualization of noisy data.

We examine different sampling lattices and their respective bandlimited spaces for reconstruction of irregularly sampled multidimensional images. Considering an irregularly sampled dataset, we demonstrate that the non-tensor-product bandlimited approximations corresponding to the body-centered cubic and face-centered cubic lattices provide a more accurate reconstruction than the tensor-product bandlimited approximation associated with the commonly-used Cartesian lattice. Our practical algorithm uses multidimensional sinc functions that are tailored to these lattices and a regularization scheme that provides a variational framework for efficient implementation. Using a number of synthetic and real data sets we record improvements in the accuracy of reconstruction in a practical setting.

The two volume set LNCS 10072 and LNCS 10073 constitutes the refereed proceedings of the 12th International Symposium on Visual Computing, ISVC 2016, held in Las Vegas, NV, USA in December 2016. The 102 revised full papers and 34 poster papers presented in this book were carefully reviewed and selected from 220 submissions. The papers are organized in topical sections: Part I (LNCS 10072) comprises computational bioimaging; computer graphics; motion and tracking; segmentation; pattern recognition; visualization; 3D mapping; modeling and surface reconstruction; advancing autonomy for aerial robotics; medical imaging; virtual reality; computer vision as a service; visual perception and robotic systems; and biometrics. Part II (LNCS 9475): applications; visual surveillance; computer graphics; and virtual reality.

We present a variational framework for the reconstruction of irregularly-sampled volumetric data in, nontensor-product, spline spaces. Motivated by the sampling-theoretic advantages of body centered cubic (BCC) lattice, this paper examines the BCC lattice and its associated box spline spaces in a variational setting. We introduce a regularization scheme for box splines that allows us to utilize the BCC lattice in a variational reconstruction framework. We demonstrate that by choosing the BCC lattice over the commonly-used Cartesian lattice, as the shift-invariant representation, one can increase the quality of signal reconstruction. Moreover, the computational cost of the reconstruction process is reduced in the BCC framework due to the smaller bandwidth of the system matrix in the box spline space compared to the corresponding tensor-product B-spline space. The improvements in accuracy are quantified numerically and visualized in our experiments with synthetic as well as real biomedical datasets.

We present a geometric framework for explicit derivation of multivariate sampling functions (sinc) on multidimensional lattices. The approach leads to a generalization of the link between sinc functions and the Lagrange interpolation in the multivariate setting. Our geometric approach also provides a frequency partition of the spectrum that leads to a nonseparable extension of the 1-D Shannon (sinc) wavelets to the multivariate setting. Moreover, we propose a generalization of the Lanczos window function that provides a practical and unbiased approach for signal reconstruction on sampling lattices. While this framework is general for lattices of any dimension, we specifically characterize all 2-D and 3-D lattices and show the detailed derivations for 2-D hexagonal body-centered cubic (BCC) and face-centered cubic (FCC) lattices. Both visual and numerical comparisons validate the theoretical expectations about superiority of the BCC and FCC lattices over the commonly used Cartesian lattice.

We present a quasi interpolation framework that attains the optimal approximation-order of Voronoi splines for reconstruction of volumetric data sampled on general lattices. The quasi interpolation framework of Voronoi splines provides an unbiased reconstruction method across various lattices. Therefore this framework allows us to analyze and contrast the sampling-theoretic performance of general lattices, using signal reconstruction, in an unbiased manner. Our quasi interpolation methodology is implemented as an efficient FIR filter that can be applied online or as a preprocessing step. We present visual and numerical experiments that demonstrate the improved accuracy of reconstruction across lattices, using the quasi interpolation framework.

The Body-Centered Cubic (BCC) and Face-Centered Cubic (FCC) lattices have been analytically shown to be more efficient sampling lattices than the traditional Cartesian Cubic (CC) lattice, but there has been no estimate of their visual comparability. Two perceptual studies (each with N = 12 participants) compared the visual quality of images rendered from BCC and FCC lattices to images rendered from the CC lattice. Images were generated from two signals: the commonly used Marschner-Lobb synthetic function and a computed tomography scan of a fish tail. Observers found that BCC and FCC could produce images of comparable visual quality to CC, using 30-35 percent fewer samples. For the images used in our studies, the L(2) error metric shows high correlation with the judgement of human observers. Using the L(2) metric as a proxy, the results of the experiments appear to extend across a wide range of images and parameter choices.

We introduce a framework for construction of non-separable multivariate splines that are geometrically tailored for general sampling lattices. Voronoi splines are B-spline-like elements that inherit the geometry of a sampling lattice from its Voronoi cell and generate a lattice-shift-invariant spline space for approximation in Rd. The spline spaces associated with Voronoi splines have guaranteed approximation order and degree of continuity. By exploiting the geometric properties of Voronoi polytopes and zonotopes, we establish the relationship between Voronoi splines and box splines which are used for a closed-form characterization of the former. For Cartesian lattices, Voronoi splines coincide with tensor-product B-splines and for the 2-D hexagonal lattice, the proposed approach offers a reformulation of hex-splines in terms of multi-box splines. While the construction is for general multidimensional lattices, we particularly characterize bivariate and trivariate Voronoi splines for all 2-D and 3-D lattices and specifically study them for body centered cubic and face centered cubic lattices.

We demonstrate that non-separable box splines deployed on body centered cubic lattices (BCC) are suitable for fast evaluation on present graphics hardware. Therefore, we develop the linear and quintic box splines using a piecewise polynomial (pp)-form as opposed to their currently known basis (B)-form. The pp-form lends itself to efficient evaluation methods such as de Boor's algorithm for splines in box splines basis. Further on, we offer a comparison of quintic box splines with the only other interactive rendering available on BCC lattices that is based on separable kernels for interleaved Cartesian cubic (CC) lattices. While quintic box splines result in superior quality, interleaved CC lattices are still faster, since they can take advantage of the highly optimized circuitry for CC lattices, as it is the case in graphics hardware nowadays. This result is valid with and without prefiltering. Experimental results are shown for both a synthetic phantom and data from optical projection tomography. We provide shader code to ease the adaptation of box splines for the practitioner. (C) 2010 Elsevier Ltd. All rights reserved.

This paper introduces a quasi-interpolation method for reconstruction of data sampled on the Body Centered Cubic (BCC) lattice. The reconstructions based on this quasi-interpolation achieve the optimal approximation order offered by the shifts of the quintic box spline on the BCC lattice. We also present a local FIR filter that is used to filter the data for quasi-interpolation. We document the improved quality and fidelity of reconstructions after employing the introduced quasi-interpolation method. Finally the resulting quasi-interpolation on the BCC sampled data are compared to the corresponding quasi-interpolation method on the Cartesian sampled data.

We introduce and analyze an efficient reconstruction algorithm for FCC-sampled data. The reconstruction is based on the 6-direction box spline that is naturally associated with the FCC lattice and shares the continuity and approximation order of the triquadratic B-spline. We observe less aliasing for generic level sets and derive special techniques to attain the higher evaluation efficiency promised by the lower degree and smaller stencil-size of the C1 6-direction box spline over the triquadratic B-spline.

Intraventricular schwannoma remains a rare entity in the literature. Controversy exists on the possible pathogenesis of such a tumor within cerebral ventricles. Literature is sparse on tumor characteristics and differences between pediatric and adult patients. We present a case of intraventricular schwannoma in a 9-year-old patient presenting with headache, hemiparesis, and focal seizure. Brain CT scan and MRI revealed an intraventricular tumor within left atrium of lateral ventricle. The patient underwent total resection of the tumor via posterior parietal approach. Histopathological exam was in favor of schwannoma. Postoperative brain MRI and MRS showed no recurrence after 18 months. Our review of the literature indicates there are some significant differences between pediatric and adult cases in different aspects including gender predominance, intraventricular location, malignant transformation, tendency for recurrence, and surgical outcome. This needs to be taken into account in the literature.

Signal reconstruction from the smallest possible Fourier measurements has been a key motivation in the compressed sensing research. We present an approach that exploits the interdependency and structural sparsity of partial derivatives for lowering the sampling rates necessary for accurate reconstruction. Our experiments show that for signals that are sparse in the gradient domain our proposed method significantly outperforms the existing approaches including the total variation (TV) based CS reconstruction.

Limited-data Computed Tomography (CT) presents challenges for image reconstruction algorithms and has been an active topic of research aiming at reducing the exposure to X-ray radiation. We present a novel formulation for tomo-graphic reconstruction based on sparse approximation of the image gradients from projection data. Our approach leverages the interdependence of the partial derivatives to impose an additional curl-free constraint on the optimization problem. The image is then reconstructed using a Poisson solver. The experimental results show that, compared to total variation methods, our new formulation improves the accuracy of reconstruction significantly in few-view settings.

Compressed Sensing (CS) for the acceleration of MR scans has been widely investigated in the past decade. Lately, considerable progress has been made in achieving similar speed ups in acquiring multi-shell high angular resolution diffusion imaging (MS-HARDI) scans. Existing approaches in this context were primarily concerned with sparse reconstruction of the diffusion MR signal \(S({\mathbf {q}})\) in the \({\mathbf {q}}\)-space. More recently, methods have been developed to apply the compressed sensing framework to the 6-dimensional joint \(({\mathbf {k}},{\mathbf {q}})\)-space, thereby exploiting the redundancy in this 6D space. To guarantee accurate reconstruction from partial MS-HARDI data, the key ingredients of compressed sensing that need to be brought together are: (1) the function to be reconstructed needs to have a sparse representation, and (2) the data for reconstruction ought to be acquired in the dual domain (i.e., incoherent sensing) and (3) the reconstruction process involves a (convex) optimization.

Visualization of volumetric data is ubiquitous in data analysis and has been widely used for exploration in scientific simulations and biomedical imaging. While direct and indirect visualization algorithms are employed extensively in applications, the visual exploration of features in the volumetric data is still a laborious task. We present an algorithm to extract exemplar isosurfaces from a 3D scalar field data set and provide the user with a representative visualization of the data. The presented approach provides an interactive tool that aids in visual analysis and exploration tasks. Our experiments on a number of benchmark data sets suggest that, compared to existing methods, the proposed approach provides a more distinct set of isosurfaces that are more representative of the complexity of the data sets.

In a few-view or limited-angle computed tomography (CT), where the number of measurements is far fewer than image unknowns, the reconstruction task is an ill-posed problem. We present a spline-based sparse tomographic reconstruction algorithm where content-adaptive patch sparsity is integrated into the reconstruction process. The proposed method leverages closed-form Radon transforms of tensor-product B-splines and non-separable box splines to improve the accuracy of reconstruction afforded by higher order methods. The experiments show that enforcing patch-based sparsity, in terms of a learned dictionary, on higher order spline representations, outperforms existing methods that utilize pixel-basis for image representation as well as those employing wavelets as sparsifying transform.

We present a study of linear interpolation when applied to uncertain data. Linear interpolation is a key step for isosurface extraction algorithms, and the uncertainties in the data lead to non-linear variations in the geometry of the extracted isosurface. We present an approach for deriving the probability density function of a random variable modeling the positional uncertainty in the isosurface extraction. When the uncertainty is quantified by a uniform distribution, our approach provides a closed-form characterization of the mentioned random variable. This allows us to derive, in closed form, the expected value as well as the variance of the level-crossing position. While the former quantity is used for constructing a stable isosurface for uncertain data, the latter is used for visualizing the positional uncertainties in the expected isosurface level crossings on the underlying grid.

We present a spline-based sparse tomographic reconstruction framework. The proposed method utilizes the closed-form analytical Radon transform of B-splines and box splines of any order and integrates the (transform-domain) sparsity of the image into the reconstruction algorithm. Our experiments show that the synergy of sparse reconstruction together with higher order basis functions (e.g., cubic B-splines) improves the accuracy of the reconstruction. This gain can also be exploited for reducing the number of projection angles in the data acquisition.

In this paper, we present a novel dictionary learning framework for data lying on the manifold of square root densities and apply it to the reconstruction of diffusion propagator (DP) fields given a multi-shell diffusion MRI data set. Unlike most of the existing dictionary learning algorithms which rely on the assumption that the data points are vectors in some Euclidean space, our dictionary learning algorithm is designed to incorporate the intrinsic geometric structure of manifolds and performs better than traditional dictionary learning approaches when applied to data lying on the manifold of square root densities. Non-negativity as well as smoothness across the whole field of the reconstructed DPs is guaranteed in our approach. We demonstrate the advantage of our approach by comparing it with an existing dictionary based reconstruction method on synthetic and real multi-shell MRI data.

This work derives a family of dilation matrices for the body-centered cubic (BCC) lattice, which is optimal in the sense of spectral sphere packing. While satisfying the necessary conditions for dilation, these matrices are all cube roots of an integer scalar matrix. This property offers theoretical advantages for construction of wavelet functions in addition to the practical advantages when iterating through a perfect reconstruction filter bank based on BCC downsampling. Lastly, we factor the BCC matrix into two matrices that allow us to cascade two two-channel perfect reconstruction filter banks in order to construct a four-channel perfect reconstruction filter bank based on BCC downsampling.

B-splines are attractive basis functions for the continuous-domain representation of biomedical images and volumes. In this paper, we prove that the extended family of box splines are closed under the Radon transform and derive explicit formulae for their transforms. Our results are general; they cover all known brands of compactly-supported box splines (tensor-product B-splines, separable or not) in any number of dimensions. The proposed box spline approach extends to non-Cartesian lattices used for discretizing the image space. In particular, we prove that the 2-D Radon transform of an N-direction box spline is generally a (nonuniform) polynomial spline of degree N - 1. The proposed framework allows for a proper discretization of a variety of tomographic reconstruction problems in a box spline basis. It is of relevance for imaging modalities such as X-ray computed tomography and cryo-electron microscopy. We provide experimental results that demonstrate the practical advantages of the box spline formulation for improving the quality and efficiency of tomographic reconstruction algorithms.

This paper exploits the power of optimal sampling lattices in tomography based reconstruction of the diffusion propagator in diffusion weighted magnetic resonance imaging (DW-MRI). Optimal sampling leads to increased accuracy of the tomographic reconstruction approach introduced by Pickalov and Basser [1]. Alternatively, the optimal sampling geometry allows for further reducing the number of samples while maintaining the accuracy of reconstruction of the diffusion propagator. The optimality of the proposed sampling geometry comes from the information theoretic advantages of sphere packing lattices in sampling multidimensional signals. These advantages are in addition to those accrued from the use of the tomographic principle used here for reconstruction. We present comparative results of reconstructions of the diffusion propagator using the Cartesian and the optimal sampling geometry for synthetic and real data sets.

B-splines are attractive basis functions for the continuous-domain representation of biomedical images and volumes. In this paper, we prove that the extended family of box splines are closed under the Radon transform and derive explicit formulae for their transforms. Our results are general; they cover all known brands of compactly-supported box splines (tensor-product B-splines, separable or not) in any dimensions. In particular, we prove that the 2-D Radon transform of an N-direction box spline is generally a (non-uniform) polynomial spline of degree N − 1. The proposed framework allows for a proper discretization of a variety of 2-D and 3-D tomographic reconstruction problems in a box spline basis. It is of relevance for imaging modalities such as X-ray computed tomography and 3-D cryo-electron microscopy.